TAMPA — To a college freshman quarterback with both a Heisman Trophy and national title on his résumé, an exhibition baseball game would be rank as cool but not spectacular, you might think. Yet to watch and listen to Jameis Winston on Tuesday at Steinbrenner Field, you could feel just how much this meant to him.

“It was surreal,” Winston said, after his Florida State team fell to the Yankees, 8-3. “Probably better than winning the national championship.”

He added: “Auburn wasn’t my favorite team growing up, but the Yankees definitely were. So this is obviously better.”

Winston led the Seminoles to a 34-31 victory over Auburn on Jan. 6 to capture the BCS crown.

Winston didn’t pitch against the Yankees, as hoped. Seminoles head coach Mike Martin said the right-hander (and switch-hitter) was “a little tender” in his previous outing, Feb. 22 against Georgia. He entered the game in the bottom of the fifth in left field and came to bat twice, grounding out to second base against Shane Greene and striking out looking against Bryan Mitchell. A left index finger injury from football season has hindered his hitting.

More meaningful to him, it seemed, was getting to meet Derek Jeter and Mark Teixeira and their retired Yankees teammate Jorge Posada. Now that he has met his childhood favorites Jeter and Ken Griffey Jr., Winston said, “I think my life is complete.”

On the field, he did little to promote the idea he could follow in the footsteps of Bo Jackson and Deion Sanders and become a two-sport star; he received his biggest cheer when he broke his wood bat during his first trip to the plate.

Yet he’s clearly thinking about it, and his football head coach Jimbo Fisher — who threw out the ceremonial first pitch — said he supported Winston’s ambition.

“I’m just 20 years old, living my life, man,” Winston said. “I want to play both as long as I can.”

Fisher told reporters: “I love two- and three-sport guys. I think you learn to compete in different ways. Each sport is different.

“Baseball is very good, especially for a quarterback, because it’s a game of failure. You’re going to fail a lot, and to be able to respond right back and be able to handle a different temperament, I think it actually helps their development.”

While Winston obviously is a pro football prospect, his baseball future remains unclear. One major league scout noted Winston “does throw hard,” so continued development could propel him onto clubs’ radars.

The baseball head coach Martin, asked whether he considered Winston to be a potential major leaguer, replied, “Oh, I really do. I truly do. If you see him throw, you’ll see why I say that.”

“The times have changed. I know it was easier back then to play both sports,” said Winston, who has met Jackson and spoken with Sanders. “But I haven’t changed. Athletes have changed, mentalities have changed, but my mentality is still the same.”